A case study is required for development of different digital versions of band-pass filter corresponding to its analogue prototype described by the following normalised transfer function:

You are to develop two different digital implementations of such filter and perform a comparative study as described in the following tasks:

1. Develop a digital implementation of the analogue prototype using impulse invariant method.

2. Develop a digital implementation of the analogue prototype using bi-linear transform.

3. Compare the two methods discussing their advantages and disadvantages. Make a preferential judgement and justify your choice.

For the tasks 1 and 2 outline the methods involved in digital design, obtain digital transfer functions, difference equations, and draw a schematic design diagrams in the Direct Form I and Direct Form II. Write down an expression for a digital filter frequency response for each task.